%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:37:52 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 40 ( 36 unt; 0 nHn; 7 RR)
% Number of literals : 51 ( 50 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(single_axiom,axiom,
divide(divide(identity,X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(inverse,axiom,
inverse(X1) = divide(identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(c_0_5,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_6,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_7,axiom,
divide(divide(identity,X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
single_axiom ).
cnf(c_0_8,plain,
multiply(divide(identity,X1),X1) = identity,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
multiply(divide(identity,X1),X2) = divide(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_5]),c_0_6]) ).
cnf(c_0_10,plain,
divide(X1,identity) = multiply(X1,identity),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_11,plain,
multiply(identity,identity) = identity,
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_12,plain,
multiply(identity,X1) = multiply(X1,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_10]) ).
cnf(c_0_13,plain,
multiply(multiply(identity,X1),X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_6]),c_0_6]) ).
cnf(c_0_14,plain,
multiply(identity,divide(identity,X1)) = divide(identity,X1),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_15,plain,
divide(X1,multiply(identity,X2)) = multiply(X1,divide(identity,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_16,plain,
multiply(X1,divide(identity,X2)) = divide(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_9]) ).
cnf(c_0_17,plain,
multiply(multiply(X1,identity),X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,plain,
divide(divide(identity,divide(divide(divide(X1,X2),X3),X1)),multiply(divide(X3,X4),X2)) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_6]) ).
cnf(c_0_19,plain,
divide(X1,multiply(identity,X2)) = divide(X1,X2),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
multiply(X1,multiply(identity,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_6]),c_0_6]) ).
cnf(c_0_21,plain,
multiply(X1,multiply(X2,identity)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_17]),c_0_13]) ).
cnf(c_0_22,plain,
multiply(identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_18]) ).
cnf(c_0_23,plain,
divide(multiply(identity,X1),X2) = divide(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_20]),c_0_9]) ).
cnf(c_0_24,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_20]),c_0_13]),c_0_13]) ).
cnf(c_0_25,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).
cnf(c_0_26,plain,
divide(X1,multiply(X2,divide(divide(X1,X2),X3))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_5]),c_0_6]),c_0_23]),c_0_24]) ).
cnf(c_0_27,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_10,c_0_25]) ).
cnf(c_0_28,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_30,plain,
divide(divide(X1,X2),X3) = divide(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
c_0_29 ).
cnf(c_0_32,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_33,plain,
multiply(X1,divide(X2,multiply(multiply(X3,X1),X4))) = divide(X2,multiply(X3,X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_26]),c_0_30]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( multiply(identity,a2) != a2
| multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_9]),c_0_5]),c_0_32]),c_0_9]),c_0_5]),c_0_32]),c_0_9]),c_0_5])]) ).
cnf(c_0_35,plain,
multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_33]),c_0_30]),c_0_28]) ).
cnf(c_0_36,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_24]),c_0_24])]),c_0_22])]) ).
cnf(c_0_37,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_38,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_24]),c_0_35]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 19:59:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % new_bool_3 with pid 465677 completed with status 0
% 0.11/0.45 % Result found by new_bool_3
% 0.11/0.45 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % SubtermCWHack with pid 465683 completed with status 0
% 0.11/0.45 % Result found by SubtermCWHack
% 0.11/0.45 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % Preprocessing time : 0.001 s
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Unsatisfiable
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 5
% 0.11/0.45 % Removed by relevancy pruning/SinE : 0
% 0.11/0.45 % Initial clauses : 5
% 0.11/0.45 % Removed in clause preprocessing : 0
% 0.11/0.45 % Initial clauses in saturation : 5
% 0.11/0.45 % Processed clauses : 228
% 0.11/0.45 % ...of these trivial : 72
% 0.11/0.45 % ...subsumed : 79
% 0.11/0.45 % ...remaining for further processing : 76
% 0.11/0.45 % Other redundant clauses eliminated : 0
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 1
% 0.11/0.45 % Backward-rewritten : 48
% 0.11/0.45 % Generated clauses : 1824
% 0.11/0.45 % ...of the previous two non-redundant : 1304
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 0
% 0.11/0.45 % Paramodulations : 1824
% 0.11/0.45 % Factorizations : 0
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 0
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 2936
% 0.11/0.45 % ...of those cached : 1961
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 27
% 0.11/0.45 % Positive orientable unit clauses : 23
% 0.11/0.45 % Positive unorientable unit clauses: 4
% 0.11/0.45 % Negative unit clauses : 0
% 0.11/0.45 % Non-unit-clauses : 0
% 0.11/0.45 % Current number of unprocessed clauses: 557
% 0.11/0.45 % ...number of literals in the above : 557
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 49
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 0
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 0
% 0.11/0.45 % Non-unit clause-clause subsumptions : 0
% 0.11/0.45 % Unit Clause-clause subsumption calls : 25
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 166
% 0.11/0.45 % BW rewrite match successes : 134
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 16114
% 0.11/0.45 % Search garbage collected termcells : 11
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.020 s
% 0.11/0.45 % System time : 0.003 s
% 0.11/0.45 % Total time : 0.023 s
% 0.11/0.45 % Maximum resident set size: 3636 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.021 s
% 0.11/0.45 % System time : 0.008 s
% 0.11/0.45 % Total time : 0.029 s
% 0.11/0.45 % Maximum resident set size: 4864 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------